Problem: Solve for $x$ and $y$ using substitution. ${3x-2y = -1}$ ${y = -x+3}$
Explanation: Since $y$ has already been solved for, substitute $-x+3$ for $y$ in the first equation. ${3x - 2}{(-x+3)}{= -1}$ Simplify and solve for $x$ $3x+2x - 6 = -1$ $5x-6 = -1$ $5x-6{+6} = -1{+6}$ $5x = 5$ $\dfrac{5x}{{5}} = \dfrac{5}{{5}}$ ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {y = -x+3}\thinspace$ to find $y$ ${y = -}{(1)}{ + 3}$ $y = -1 + 3$ $y = 2$ You can also plug ${x = 1}$ into $\thinspace {3x-2y = -1}\thinspace$ and get the same answer for $y$ : ${3}{(1)}{ - 2y = -1}$ ${y = 2}$